Wiring up your pot

Leave your LED connected, and
wire the pot up to the Arduino like this.

The black wire connects
the left terminal of the pot to Gnd (ground).

The red wire connects to the Arduino's 5v.

The third wire connects the pot's middle terminal to
the Arduino's analog input pin 0.
(The colors aren't important -- you can use any colors you like.)

The Arduino will be able to read the voltage and watch it change
as you twist the knob.

Analog Input sketch

To try it out, find File->Examples->03.Analog->AnalogInput
and upload that sketch.

Now twiddle the dial. What happens?

The sketch is reading an analog value from analog pin 0, like this:

sensorValue = analogRead(sensorPin);

sensorValue is a variable that holds whatever value was read in.
You can use sensorValue later in the program to do things like decide
how long to delay between flashes.

Other things to try

You can do analog output, too, to
make the LED brighter or dimmer. Once you have this sketch working,
go to the analog output page
to see how that works, and to find out how you can use the serial
console for debugging.